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## Question 3 Consider \( f(x) = 4x + \frac{3}{x} \). For this function, there are four important open intervals: \((- \infty, A)\), \((A, B)\), \((B, C)\), and \((C, \infty)\). \( A \) and \( C \) are critical numbers and \( f(x) \) is undefined at \( B \). - \( A = \, \underline{\hspace{2cm}} \) - \( B = \, \underline{\hspace{2cm}} \) - \( C = \, \underline{\hspace{2cm}} \) Type your answers for \( A, B, C \), to the nearest hundredth (two decimal places). ### Determine the Behavior of \( f(x) \) Is \( f(x) \) increasing (INC) or decreasing (DEC) or constant (CON) on the interval? \((- \infty, A)\) \(\underline{\hspace{5cm}}\) \((A, B)\) \(\underline{\hspace{5cm}}\) \((B, C)\) \(\underline{\hspace{5cm}}\) \((C, \infty)\) \(\underline{\hspace{5cm}}\) Type in INC for increasing, DEC for decreasing, or CON for constant. ### Concavity of \( f(x) \) Is \( f(x) \) concave up or concave down on \((- \infty, 0)\)? \(\underline{\hspace{5cm}}\) Is \( f(x) \) concave up or concave down on \((0, \infty)\)? \(\underline{\hspace{5cm}}\) Type in CCD for concave down or CCU for concave up.

## Question 3 Consider \( f(x) = 4x + \frac{3}{x} \). For this function, there are four important open intervals: \((- \infty, A)\), \((A, B)\), \((B, C)\), and \((C, \infty)\). \( A \) and \( C \) are critical numbers and \( f(x) \) is undefined at \( B \). - \( A = \, \underline{\hspace{2cm}} \) - \( B = \, \underline{\hspace{2cm}} \) - \( C = \, \underline{\hspace{2cm}} \) Type your answers for \( A, B, C \), to the nearest hundredth (two decimal places). ### Determine the Behavior of \( f(x) \) Is \( f(x) \) increasing (INC) or decreasing (DEC) or constant (CON) on the interval? \((- \infty, A)\) \(\underline{\hspace{5cm}}\) \((A, B)\) \(\underline{\hspace{5cm}}\) \((B, C)\) \(\underline{\hspace{5cm}}\) \((C, \infty)\) \(\underline{\hspace{5cm}}\) Type in INC for increasing, DEC for decreasing, or CON for constant. ### Concavity of \( f(x) \) Is \( f(x) \) concave up or concave down on \((- \infty, 0)\)? \(\underline{\hspace{5cm}}\) Is \( f(x) \) concave up or concave down on \((0, \infty)\)? \(\underline{\hspace{5cm}}\) Type in CCD for concave down or CCU for concave up.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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## Question 3 Consider \( f(x) = 4x + \frac{3}{x} \). For this function, there are four important open intervals: \((- \infty, A)\), \((A, B)\), \((B, C)\), and \((C, \infty)\). \( A \) and \( C \) are critical numbers and \( f(x) \) is undefined at \( B \). - \( A = \, \underline{\hspace{2cm}} \) - \( B = \, \underline{\hspace{2cm}} \) - \( C = \, \underline{\hspace{2cm}} \) Type your answers for \( A, B, C \), to the nearest hundredth (two decimal places). ### Determine the Behavior of \( f(x) \) Is \( f(x) \) increasing (INC) or decreasing (DEC) or constant (CON) on the interval? \((- \infty, A)\) \(\underline{\hspace{5cm}}\) \((A, B)\) \(\underline{\hspace{5cm}}\) \((B, C)\) \(\underline{\hspace{5cm}}\) \((C, \infty)\) \(\underline{\hspace{5cm}}\) Type in INC for increasing, DEC for decreasing, or CON for constant. ### Concavity of \( f(x) \) Is \( f(x) \) concave up or concave down on \((- \infty, 0)\)? \(\underline{\hspace{5cm}}\) Is \( f(x) \) concave up or concave down on \((0, \infty)\)? \(\underline{\hspace{5cm}}\) Type in CCD for concave down or CCU for concave up.
Transcribed Image Text:## Question 3 Consider \( f(x) = 4x + \frac{3}{x} \). For this function, there are four important open intervals: \((- \infty, A)\), \((A, B)\), \((B, C)\), and \((C, \infty)\). \( A \) and \( C \) are critical numbers and \( f(x) \) is undefined at \( B \). - \( A = \, \underline{\hspace{2cm}} \) - \( B = \, \underline{\hspace{2cm}} \) - \( C = \, \underline{\hspace{2cm}} \) Type your answers for \( A, B, C \), to the nearest hundredth (two decimal places). ### Determine the Behavior of \( f(x) \) Is \( f(x) \) increasing (INC) or decreasing (DEC) or constant (CON) on the interval? \((- \infty, A)\) \(\underline{\hspace{5cm}}\) \((A, B)\) \(\underline{\hspace{5cm}}\) \((B, C)\) \(\underline{\hspace{5cm}}\) \((C, \infty)\) \(\underline{\hspace{5cm}}\) Type in INC for increasing, DEC for decreasing, or CON for constant. ### Concavity of \( f(x) \) Is \( f(x) \) concave up or concave down on \((- \infty, 0)\)? \(\underline{\hspace{5cm}}\) Is \( f(x) \) concave up or concave down on \((0, \infty)\)? \(\underline{\hspace{5cm}}\) Type in CCD for concave down or CCU for concave up.
Expert Solution
Step 1

Consider the function 

f(x)=4x+3x

Four important intervals 

−∞,A,A,B,B,C,C,∞

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